Evaluating solvation entropies directly and combining with direct energy calculations is one way of calculating free energies of solvation and is used by Inhomogeneous Fluid Solvation Theory (IFST). The configurational entropy of a fluid is a function of the interatomic correlations and can thus be expressed in terms of correlation functions. The entropies in this work are directly calculated from a truncated series of integrals over these correlation functions. Many studies truncate all terms higher than solvent- solute correlation. This study includes an additional solvent-solvent correlation term and assesses the associated free energy when IFST is applied to a fixed Lennard-Jones particle solvated in neon. The strength of the central potential is varied to imitate larger solutes. Average free energy estimates with both levels of IFST theory are able to reproduce the estimate made using Free energy Perturbation (FEP) to within 0.16 kcal/mol. We find that the signal from the solvent-solvent correlations is very weak. Our conclusion is that for monatomic fluids simulated by pairwise classical potentials the correction term is relatively small in magnitude. This study shows it is possible to reproduce the free energy from a path based method like FEP, by only considering the endpoints of the path. This method can be directly applied to more complex solutes which break the spherical symmetry of this study.